IIARD International Institute of Academic Research and Development

INTERNATIONAL JOURNAL OF APPLIED SCIENCES AND MATHEMATICAL THEORY (IJASMT )

E- ISSN 2489-009X
P- ISSN 2695-1908
VOL. 11 NO. 3 2025
DOI: 10.56201/ijasmt.vol.11.no3.2025.pg71.83

---

Application of Runge-Kutta to Solving the Nonlinear Ordinary Differential Equation of a Deformed Cylindrical Compressible Blatz-Ko Material Under Torsional Effects.

Egbuhuzor Udechukwu Peter, and Udoh Ndipmong Augustine

---

Abstract

This paper discussed the homogeneous, isotropic, compressible nonlinearly elastic cylindrical Blatz-Ko material deforming under pure torsion. The mathematical model of the radial deformation of the structure resulted into a highly nonlinear second-order ordinary differential equation with boundary conditions and the solution was obtained using Runge-Kutta fourth order method and implemented using MATLAB software. The results show that deformations decrease towards the origin and a decrease in volume is observed. The effects of stress and applied pressure on the material under study were compared and results showed that the stress increased as the radius of the material decreases.

keywords:

Blatz-Ko, Matlab, Runge-Kutta, Stress, Deformation, Hyperelastic, Material, mechanics, Isotropic, and compressible

---

References:

Bechir, H., Chevalier, L., Chaouche, M., &Boufala, K. (2006). Hyperelastic constitutive model for
rubber-like materials based on the first Seth strain measures invariant. European Journal
of Mechanics-A/Solids, 25(1), 110-124.
Chibueze, B. E., & Julius, E. B. (2021). Deformation of Incompressible Hollow Cylindrical
Structure Loaded by Azimuthal Shear. Asian Research Journal of Current Science, 95-
Currie, P. K., & Hayes, M. (1981). On non-universal finite elastic deformations. In Proceedings
of the IUTAM Symposium on Finite Elasticity: Held at Lehigh University, Bethlehem, PA,
USA August 10–15, 1980 (pp. 143-150). Dordrecht: Springer Netherlands.
Jiang, X., & Ogden, R. W. (2000). Some new solutions for the axial shear of a circular cylindrical
tube
of
compressible
elastic
material. International
journal
of
non-linear
mechanics, 35(2), 361-369.
Kassianidis, F., Ogden, R. W., Merodio, J., & Pence, T. J. (2008). Azimuthal shear of a
transversely isotropic elastic solid. Mathematics and Mechanics of Solids, 13(8), 690-724.
Kirkinis, E., & Ogden, R. (2002). On extension and torsion of a compressible elastic circular
cylinder. Mathematics and Mechanics of Solids, 7(4), 373-392.
Polignone, D. A., &Horgan, C. O. (1991). Pure torsion of compressible non-linearly elastic circular
cylinders. Quarterly of applied mathematics, 49(3), 591-607.
Rivlin, R. S. (1997). Large Elastic Deformations of Isotropic Materials: VI. Further Results in the
Theory of Torsion, Shear and Flexure (pp. 120-142). Springer New York.
Shrivastava, S. C., Jonas, J. J., & Canova, G. (1982). Equivalent strain in large deformation torsion
testing: theoretical and practical considerations. Journal of the Mechanics and Physics of
Solids, 30(1-2), 75-90.
Valiollahi, A., Shojaeifard, M., &Baghani, M. (2019). Closed form solutions for large deformation
of cylinders under combined extension-torsion. International Journal of Mechanical
Sciences, 157, 336-347.

DOWNLOAD PDF

---

Back